Eoin Doyle had an early chance to open the scoring for the visitors, but after latching on to a ball over the top, he fired wide of the post.
© Getty Images
They continued to dominate and Antoni Sarsevic came close with a strike that he drilled just wide.
They doubled their lead three minutes later, when Sam Morsy curled a strike from the edge of the box into the back of the net.
Doyle came close to grabbing a third when his chipped effort beat Scott Davies in the Fleetwood goal, but dropped wide of the post.
After the break Jimmy Ryan restored Chesterfield's two-goal advantage, when he fired an effort from long-range into the bottom corner.
Ritchie Humphreys denied Parkin from scoring a second goal for the home side, after blocking his close-range effort.
Fleetwood came close again in stoppage time, when Alan Goodall rose highest to meet a corner, but he could only head the ball over the bar.
The second leg will take place at the Proact Stadium on February 17.